Chef has been exploring prime numbers lately, and has recently made a conjecture resembling
one of Goldbach's conjectures.
Chef's conjecture is that any odd number greater than 61 can be expressed as the sum of
a prime, a square of a prime, and a cube of a prime.
He wants you to help verify his conjecture for small numbers.
Note: negative numbers are never considered to be prime, nor are 0 and 1.

------ Input ------

Input will consist of a series of odd numbers greater than 61 and less than 10^{6},
one per line, terminated by the number 0 on a line by itself.
There will be at most 1000 lines.

------ Output ------

For each odd number in the input, print 3 primes P_{1}, P_{2}, P_{3} on a line,
where P_{1} + P_{2}^{2} + P_{3}^{3} is equal to the number from the input.
If no such primes exist, print "0 0 0" instead (quotes for clarity).
If there are multiple triplets of primes that satisfy the equation, print any such triplet.

----- Sample Input 1 ------
81
85
155
0
----- Sample Output 1 ------
5 7 3
73 2 2
5 5 5

见题面

见题面